Course to steer over several hours of tide

When one hour isn’t enough

In Lesson 29 you worked a course to steer from a one-hour vector triangle: one hour of stream from the start, one hour of boat speed from the end of it, and the water track between. That is all you need for a passage of about an hour, or a little more if the stream hardly changes. Over several hours it changes a lot. As Lesson 28 showed, the stream at each diamond builds, eases, goes slack and turns, hour by hour — and on a long leg the yacht moves from one diamond’s area into another’s.

There are two ways to deal with that:

• A new course every hour. Work a one-hour triangle for each hour in turn and change course on the hour. The yacht stays on the ground track all the way.
• One course for the whole passage. Allow for every hour’s stream at once, and steer a single course from start to finish. This is the Yachtmaster-level method, and the subject of this lesson.

Lay each hour’s stream end to end from the start, then swing an arc of the whole distance you will sail through the water. The water track to the cut is one course to steer for the entire passage.

Why steer one course?

• Cross-streams that reverse cancel. If the stream sets you one way for an hour and back the other way later, one course allows only for what is left over. Correcting every hour, you would aim up-tide against each in turn.
• A shorter distance through the water. Stemming a cross-stream costs speed along the track. A straight water track is the shortest way through the water to the same place, so one course usually arrives a little sooner. The saving is small with weak streams and grows when strong ones run across your track first one way and then the other.
• Less work. One construction at the chart table instead of one every hour, and one course for the helm to hold.

The method, step by step

1. Ground track. Draw the line from the start to the destination, with two arrows, and measure its direction (°T) and length.
2. Estimate the passage time — distance ÷ boat speed through the water — to the nearest half hour. This tells you how many hours of stream to allow for; any part hour at the end is then a half.
3. Find the stream for each hour. Work out roughly where the yacht will be in each hour (at boat speed along the track) and use the diamond nearest there. Convert HW Port Kerran to BST and use the row for that hour; interpolate the rate by the day’s range, exactly as in Lesson 28. Leave on the half hour of a tidal hour — at HW−5½, say — and each hour of the passage falls on exactly one row. Otherwise use the row for the middle of each hour.
4. Lay the streams end to end from the start, three arrows each: hour one from the start, hour two from the end of hour one, and so on. A part hour at the end scales that hour’s stream: half an hour of a 1.2 kn stream is 0.6 M.
5. Swing the arc. Open the dividers to the distance you will sail through the water in the same time — hours × boat speed — and from the end of the last stream swing an arc to cut the ground track (extended if need be).
6. The water track is your course to steer. Join the end of the last stream to the cut, with one arrow, and measure it: that is the course to steer (°T) for the whole passage. Start to cut is the distance made good in that time; divided by the hours, it is your average speed over the ground.
7. Check where the arc cuts — at the destination, short of it, or beyond — and work out the passage time and ETA.
8. Then leeway, variation and deviation, exactly as in Lessons 29 and 30.

Worked example: Kerran Bay to west of Kerran Head

On Tue 1 Jun you plan to sail from WP1, 1.8 M south-south-west of Kerran Approach buoy, to WP2, 4.5 M west-north-west of Kerran Head light. The track runs between Mew Rock and the wreck and passes west of the West Ledge buoy. You will make 4.5 kn through the water and plan to leave at 0911 BST.

Had you re-planned every hour instead, the three one-hour triangles would give 328°, 320°, 310°T — a different course each hour, each aiming up-tide into that hour’s stream — and the passage would take 2 h 26 min, against 2 h 25 min on one course. With weak streams near slack water the saving is small; the work saved is not.

Short of the destination, or beyond?

The arc shows how far along the ground track you get in the time you allowed. If it cuts at the destination, your estimate was right. If it cuts short, the streams have held you back overall: the passage will take longer, and the stream in that extra time is missing from your plan. Add it — a part hour if need be — and swing a longer arc. If it cuts beyond, they have helped you along: you will arrive early, so take off the stream for time you won’t be at sea, and swing a shorter arc.

Leave the same waypoint at 1611 that afternoon (HW+1½) and the rows are 2, 3 and 4 hours after HW: 075°T 0.5 kn at A, then 160°T 0.3 kn at C, then 245°T 1.0 kn at C. With 2½ hours of stream the arc cuts 0.3 M short of WP2, because the stream is foul overall. The passage will take nearer 2 h 35 min; reworked for that time, the course changes only from 322°T to 323°T. A gap of a few tenths of a mile moves the course by a degree or so and isn’t worth reworking; a bigger one is.

The catch: off the line between the hours

One course is a straight line through the water. Over the ground the yacht goes wherever the streams so far have set her, and comes back to the ground track only at the end. Before you commit, plot where she will be at the end of each hour, as an estimated position (Lessons 14 and 30): from the last position, the water track for that hour (course to steer, boat speed × hours) and then that hour’s stream. Check those positions — and the lines between them — against the dangers on both sides.

On the morning passage the first hour’s stream sets the yacht towards the south-west, and the hours that follow bring her back. She is 0.5 M to port of the ground track at 1011 and 0.4 M to port at 1111, then back on it at WP2: on the open side. The wreck, 1.5 M from the ground track, is passed at 1.2 M, and Mew Rock at 1.3 M. That is fine.

In the afternoon the stream runs the other way. The first hour’s flood sets her north-east, and the streams that follow don’t bring her back until the end: 0.5 M to starboard of the track at 1711, 0.5 M to starboard at 1811. She would pass Mew Rock at 0.5 M and Head Ledge at 0.5 M, and pass within 0.1 M of the West Ledge buoy. The ground track itself was 0.6 M clear of that buoy.

That afternoon plan is not safe. 0.1 M off the buoy is no margin at all for errors in the stream, your speed and your steering, and the rocks the buoy guards lie just to the east of it. Don’t sail one course here: split the passage or leave at another time, as below.